Worm and worm gear arrangements have long been universally known as advantageous drive mechanisms for unilaterally transferring power and motion from one rotating gear element to another. Very simply, the mechanism comprises a worm and a worm gear, the worm having a helical thread which meshes with the teeth of the worm gear, the axes of the two elements lying at substantially right angles. Conventionally, rotation of the worm causes a corresponding rotation of the gear, neither of the elements being movable along its axis. Uses of the worm and worm gear mechanism have been as old and as broad as the mechanical arts themselves and are too numerous to list. One field in which the mechanism has proved exceptionally useful and with which the worm and worm gear arrangement of the invention is particularly concerned is that of measurement, adjustment, positioning, and the like. Because of the high degree of precision required, very fine-pitch worms and gears are there employed for the transmission of uniform angular rotation rather than power. In each of such prior art arrangements, the rotating worm transmits only a corresponding rotation to the worm gear, the latter being conventionally fixed against lateral movement along its axis as mentioned. An objective of the present invention is a new and novel worm and worm gear mechanism of general utility in which the rotation of the worm imparts to the worm gear not only a corresponding rotation but also a precise displacement of the worm gear along its axis.